The (mixed) random variable X has probability density function(pdf) fX (x) given by:
fx(x)=0.5δ(x−3)+ { c.(4-x2), 0≤x≤2
0, otherwise
where c is a constant.
(a) Sketch fX (x) and find the constant c.
(b) Find P (X > 1).
(c) Suppose that somebody tells you {X > 1} occurred. Findthe conditional pdf fX|{X>1}(x), the pdf of X giventhat {X > 1}.
(d) Find FX(x), the cumulative distribution function of X.
(e) Let Y = X2 . Find fY (y), the probability densityfunction of the random variable Y
